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Math Help - Sylow theorems

  1. #1
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    Sylow theorems

    Hello!

    I have some problems with the following exercise:

    Let G be a noncommutative group of order 12, H be a 3-Sylow group in G, and let T:G->{maps G/H->G/H}, where T(g) is defined as the map which sends aH -> gaH.

    Show that:

    1) T is not injective, if and only if H is normal in G
    2) Use 1) to prove that if H is not normal in G, then G is isomorphic to the alternating group A_4.

    Does anyone have an idea for 1) or 2)?


    Marco
    Last edited by MarcoRo; February 28th 2013 at 08:05 AM.
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